Render Environment Map with Blur Effect
If your environment texture on the icosphere is unblurred:

Render everything into 1 equirectangular environment map. Blur it in your favourite 2d app (it is seamless so tile it before blurring) or inside cycles nodes with noising the mapping inputs with b-wide node pack.

Then render this blurred environment into the cube map.

If your environment texture on the icosphere is already blurred:

Render the objects inside the icosphere only. Lit them with the environment texture but exclude the icosphere to not reflect on the cube.

Blur this equirectangular inside 2d app to match blur of the enviro and merge them into 1 environment (you will need an alpha channel for this also).

Then render a cube map from this blurred enviro.